1、Chapter 17 The Polarization of light,1 Natural light and polarized light,2 Producing and analysis of polarized light Malus law,3 Producing and analysis of polarized light by reflection and refraction of light Brewsters law,4 The phenomena of birefringencePolarizing and analyzing,1 Natural light and
2、polarized light,Longitudinal wave: the vibrating direction is back and forth along the direction of wave propagation; Transverse wave: the vibrating direction is perpendicular to the direction of wave propagation.,Plane of vibration 振动面：a plane composed of optical vector E and direction of propagati
3、on of light 通过波的传播方向并包含振动矢量在内的平面,Polarization 偏振: the vibrating directions of wave are not symmetry about the direction of propagation波的振动方向对传播方向不具有对称性,1 Polarization state of light 光的偏振态,Polarization state 偏振态：在与传播方向垂直的二维空间的振动状态,Natural light 自然光,Partial polarized light 部分偏振光,On the plane perpendic
4、ular to the direction of propagation of light 在与光的传播方向垂直的平面上,Linear polarized light线偏振光,Circular polarized light 圆偏振光,Natural light 自然光: A combination of an infinite number of photo vectors that have the same amplitude, have random vibrating directions and have not fixed phase difference,Linear pola
5、rized light (plane polarized light) 线偏振光: photo vector only vibrates along a fixed direction,Partially polarized light 部分偏振光: On the plane perpendicular to the direction of propagation of wave, the amplitudes of vibration of the different directions are different.,Plane polarized light,Plane polariz
6、ed light,Natural light,Partially polarized light,2 Natural light,On the plane perpendicular to the direction of propagation of the wave, choosing x axis and y axis：,I：the intensity of natural light自然光光强,Natural light can be resolved into two linear polarized light that are perpendicular to each othe
7、r and have half an intensity of natural light. 自然光可分解为振动方向相互垂直的两个线偏振光，其强度各占总光强的一半.,2 Producing and analysis of polarized light Malus law,1 Polarizer and analyzer Polaroid 偏振片,Polarizer 起偏器,(2) Analyzer 检偏器,An optical instrument to analyze the polari-zation state of light,An optical instrument to tur
8、n natural light into polarized light,(3) Polaroid 偏振片 Polarizer and analyzer are called polaroid,2 Malus law 马吕斯定律,I0: The intensity of polarized light to be analyzed 被检偏振光的强度,I: The intensity of light through a analyzer 通过检偏器后的光强, : The angle between the vibrating direction of linear polarized ligh
9、t and the polarizing direction of an analyzer,最大光强,最小光强,例 一束光是自然光和线偏振光的混合光，让其通过一偏振片。若以此入射光束为轴旋转偏振片，测得透射光强度最大值是最小值的5倍，求入射光束中自然光与线偏振光的光强之比。,解,设自然光强度I1，线偏振光强度I2,3 Producing and analysis of polarized light by reflection and refraction of light Brewsters law,1 The polarization reflected light Brewsters l
10、aw 光在反射时的偏振 布儒斯特定律,(1) In general： Reflected rays and refracted light are partially polarized light,(2) especially：i=i0 Reflected rays is linear polarized Refracted rays is partially polarized light i0：polarizing angle 起偏振角Brewsters angle,(3) Brewster law:,When the angle of incidence is equal to ang
11、le of polarizing angle i0, the rays reflected and refracted are perpendicular to each other.,2 Corollary 推论,当入射角等于起偏振角i0时，反射光线与折射光线互相垂直,Ex Calculate the Brewster angle for producing a linear polarized beam of light by reflection in air from a crown glass (n=1.52) surface.,3 The analysis of polarized
12、 light by reflection of light 反射检偏,The first plate plays the role of a polarizer, i.e. of an instrument producing linearly polarized light from unpolarized light; the second plays the role of an analyzer, i.e. of an instrument which detects polarized light.,以第一块镜子的反射光为轴将M2旋转90O，M2的法线也转90O检偏,经M1反射的光垂
13、直于M1的入射面；由于M2的法线转了90O，垂直于M1的入射面的光振动，对于M2来说，是平行于M2的入射面的光振动，但仍以i0入射。以i0 入射，只反射垂直于入射面的光振动检偏。,4 玻片堆 Polarizing by refraction of light 折射光起偏,例 画出反射光和折射光：,(1) The difference of Brewsters law and total reflection,Brewsters law: If light is incident under i0, the reflected light has only component perpendic
14、ular to the plane of incidence,已知 i0，n1，可求得n2,Total reflection: If i exceeds the limiting ic, no light enters the second medium.,(2) The application of Brewsters law:,4 The phenomena of birefringence Polarizing and analyzing,1 The phenomena of Birefringence 双折射现象,Homogeneity 各处均匀,Isotropy 各向同性,Aniso
15、tropy 各向异性,Birefringence: one incident ray will give rise two refracted rays in anisotropic medium,2 To explain birefringence 解释双折射现象,Questions: (1) Obey the law of refraction? 是否遵从折射定律？(2) Birefringence in all direction? 所有方向都有双折射现象？(3) How the polarization states? 偏振态如何？,一束光射在各向异性的晶体物质时，会有两条折射光线,A
16、nswer: The results of researches 研究结果： (1) 一束光满足折射定律：ordinary light o光；另一束光不满足折射定律： extraordinary light e光。 Calcite 方解石：no=1.658 ne=1.4861.658,(3) Both ordinary light and extraordinary light are linear polarized lights o光和e光都是线偏振光,Principal section 主截面： 光轴与任意天然晶面的法线所构成的平面,Principal plane 主平面： 晶体内的光线
17、与光轴所构成的平面,(2) Optical axis 光轴方向：No birefringence 无双折射,Ordinary light and extraordinary light have the same refractive index and velocity. o光和e光的折射率相同，o光和e光的传播速度相同,Ordinary light is linear polarized lights, and the vibrating direction is perpendicular to its principal plane; extraordinary light is li
18、near polarized lights, and the vibrating direction is parallel to its principal plane; o光是线偏振光, 其振动方向垂直于主平面; e光也是线偏振光, 其振动方向平行于主平面。,In general: o光的主平面与 e光的主平面不重合，o光的振动方向与 e光的振动方向不垂直。,Special case 特例： 主平面与主截面平行(重合),o光的主平面与 e光的主平面重合,o光的振动方向与 e光的振动方向相互垂直,Polarizing polarized light 检验偏振光： 在晶体外，可以用检偏器检验两
19、束光是否是偏振光，也可检验它们的偏振方向。,3 Application - Nicols prism 尼科耳棱镜,The calcite is about three times as long as it is wide,It consists of a natural calcite which is cut into two equal parts along a diagonal plane, and with the two parts cemented together with Canada balsam.,A,N,no=1.658,n加=1.55,如图入射：ne=1.516,n
20、e n加 no,在粘接面，o光可以发生全反射,线偏振光质量相当高,The end faces are ground off to reduce angle to 68o.,To analyze polarized light by Nicols prism 利用尼科耳棱镜检验偏振光：,Bright,dark,To detect linearly polarized light with a Nicol prism we only have to rotate the prism about its longitudinal axis.,I0,I,I I0 cos2,若两块尼科耳棱镜的夹角（主截面夹角）为，透过第二块尼科耳棱镜的光强：,
